In many existing applications, a chord length distribution (CLD) is used for in-line monitoring to depict a size distribution for a set of particles. However, a CLD may be an inaccurate and an imprecise measure of particle size. First, a CLD can be an inaccurate measure of particle size because measurement tools frequently inaccurately measure a particle's chord length. For example, a chord length for a first particle may be inaccurately measured as a sum of the chord length of the first particle and a chord length of a second particle located near the first particle. In addition to CLD being an inaccurate measure of particle size, CLD can also be an imprecise measure of particle size because, for each particle, a nearly infinite number of different chord lengths may be identified. Specifically, a nearly infinite number of different chord lengths may be identified for a given particle depending upon an orientation of the particle with respect to the device performing the chord length measurement. This variability in chord length for a single particle is even further compounded for a set of particles. As a result of this variability in CLD for a set of particles, CLD is an imprecise measure of particle size for a set of particles.
As a result of this inaccuracy and imprecision of a CLD as a measurement of particle size for a set of particles, it cannot easily be correlated with particle size. Specifically, one alternative to using a CLD as a measurement of particle size for a set of particles is use of a particle size distribution (PSD). In some embodiments, a PSD for a set of particles can be generated based on a CLD for the set of particles. However, existing models that are configured to generate a PSD based on a CLD are often specific to a particular type of CLD and to a specific particle morphology. In other words, an existing model that is configured to generate a PSD based on a CLD may only be able to generate a PSD based on a particular type of CLD and a particular particle morphology on which the model was previously trained and validated. There are a plurality of types of CLDs and large variation in particle morphologies in many systems of interest. Therefore, to be capable of generating a PSD for a set of particles based on a CLD of any of the plurality of CLD types, existing methods require a plurality of different models to be trained and validated. Most importantly, a different model is required for each different particle morphology.
Many particle systems exhibit large deviations in morphology during in-line CLD monitoring when morphological changes occur. Existing models that predict PSD from an in-line CLD do not work well when these morphological changes occur. These existing models are incapable of identifying a morphology for the set of particles.